Electron Screening in Muonic Atoms

Abstract

Screening corrections to the muon binding energies are computed for Pb, Tl, Ba, and O. Available methods of calculation are compared. It is shown that in a broad range of atomic charges and muon states the screening of nuclear charge by the muon is almost complete, and therefore the electron density of the $Z-1\mathrm{}$ element can be used in most applications. The effect of the muon on the electron cloud and the effect of the vacancies in electron shells on the screening corrections are calculated and discussed. The degree of ionization of the electron $1s_{\frac{1}{2}}$ orbit is determined by a cascade calculation including repopulation from the $2p$ shell.